Onset of spontaneous scalarization in spinning Gauss-Bonnet black holes

TL;DR

This paper analytically determines the critical spin parameter for the onset of spontaneous scalarization in Kerr black holes within Einstein-Gauss-Bonnet-scalar theory, confirming previous numerical results with an exact relation.

Contribution

It provides an exact analytical expression for the critical rotation parameter, advancing understanding of scalarization onset in spinning black holes.

Findings

Critical spin parameter is exactly 0.5 for scalarization onset.

Analytical proof confirms previous numerical estimates.

Boundary between bald and scalarized black holes is precisely characterized.

Abstract

It has recently been proved numerically that spinning black holes in Einstein-scalar theories which are characterized by a non-minimal negative coupling of the scalar field to the Gauss-Bonnet invariant of the curved spacetime may develop exponentially growing instabilities. Intriguingly, it has been demonstrated that this tachyonic instability, which marks the onset of the spontaneous scalarization phenomenon in the Einstein-Gauss-Bonnet-scalar theory, characterizes spinning black holes whose dimensionless angular momentum parameter ${\bar a}\equiv a/M$ is larger than some critical value ${\bar a}_{\text{crit}}\simeq0.505$. In the present paper we prove, using {\it analytical} techniques, that the critical rotation parameter which marks the boundary between bald Kerr black holes and hairy (scalarized) spinning black holes in the Einstein-Gauss-Bonnet-scalar theory is given by the exact dimensionless relation ${\bar a}_{\text{crit}}={1\over 2}$.